derivatives with respect to argument, except where
indicated otherwise.

The main functions treated in this chapter are the
Bessel functions
Jν⁡(z),
Yν⁡(z);
Hankel functions
Hν(1)⁡(z),
Hν(2)⁡(z);
modified Bessel functions
Iν⁡(z),
Kν⁡(z);
spherical Bessel functions
jn⁡(z),
yn⁡(z),
hn(1)⁡(z),
hn(2)⁡(z);
modified spherical Bessel functions
in(1)⁡(z),
in(2)⁡(z),
kn⁡(z);
Kelvin functions
berν⁡(x),
beiν⁡(x),
kerν⁡(x),
keiν⁡(x).
For the spherical Bessel functions and modified spherical Bessel functions the
order n is a nonnegative integer. For the other functions when the
order ν is replaced by n, it can be any integer. For the Kelvin
functions the order ν is always assumed to be real.

A common alternative notation for
Yν⁡(z) is Nν⁡(z).
Other notations that have been used are as follows.